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Chapter 5. Angle Modulation

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Characteristics of Angle Modulation The amplitude of an angle modulated wave is constant. The message resides in the zero crossings alone, providing the carrier frequency is large. The modulated wave does not resemble the message waveform.

Narrowband PM and FM We can expand the signal (using Taylor’s expansion) The spectrum is given by Hence, the signal has a bandwidth of 2W.

Multi-tone Consider the case of multiple tones, e.g., The modulated signal can be written as

Periodic Modulation When the signal is periodic, the Fourier series are given by The modulated signal can be written as

Transmission Bandwidth The generation and transmission of pure FM requires infinite bandwidth. Hence, our questions is: how much of the modulated signal spectrum is significant? The Bessel function falls off rapidly for There are M significant sideband pairs and 2M+1 significant lines all told. The bandwidth can be given by

Direct FM In direct FM, we use VCO to generate the frequency modulated by the signal.

Phase Modulator Although we seldom transmit a PM wave, we are still interested in phase modulators because (1) the implementation is relatively easy; (2) the carrier can be supplied by a stable frequency source; (3) integrating the input signal to a phase modulator produces an FM output.

Triangular-Wave FM Triangular-wave FM is a modern and rather novel method for frequency modulation that overcomes the inherent problems of conventional CVOs and indirect FM systems.

Frequency Detection A frequency detector, often called a discriminator, produces an output voltage that should vary linearly with the instantaneous frequency of the input. Almost every circuit falls into one of the following four categories: FM-to-AM conversion Phase-shift discrimination Zero-crossing detection Frequency feedback

FM-to-AM Conversion Any device of circuit whose output equals the time derivative of the input produces FM-to-AM conversion:

Interference Interference refers to the contamination of an information-bearing signal by another similar signal, usually from a human source. Interfering sinusoids: consider a receiver tuned to some carrier frequency. The total received signal is

Deemphasis The fact that detected FM interference is most severe at large values of |f_i| suggests a method for improving system performance with selective postdetection filtering, called deemphasis filtering.